Please help I'm so confused "Linear Inequalities"

[shorty21432]

I have a paper due tomorrow and am no where near close to being done, or even knowing how to do it. I have recently had a death in my family and missed a lot of school so I am totally lost and confused :sad: I'm totally tripping out. it says graph the linear inequalities Now I know how to graph, its just coming up with the ordered pairs. I can't solve the equations, first one is -3x+2y>orequal to 6 I hope that someone can help me I would appreciate any help i can get

 

[thedarjeeling]

Ok so you have \(\displaystyle -3x + 2y \ge 6\). Just start solving for it like a regular linear equation, but keep in mind if you ever divide/multiply by a negative number, you have to switch the direction of the inequality!!! However for this particular one, you won't have to switch the inequality, so

\(\displaystyle -3x + 2y \ge 6\)
\(\displaystyle 2y \ge 6 +3x\)
\(\displaystyle y \ge 3 +\frac{3}{2}x\)

You find the x and y intercepts like you normally would (just pretend it's an equal sign for this part). So, obviously the y intercept is 3 (plug in x=0), and I'll let you find out the x intercept (plug in y = 0).

Now when you actually graph it, notice that we have a \(\displaystyle \ge\) sign.

There are two implications:

1) Since it's greater than EQUAL to, then the line you draw will be a SOLID line (just like it is with regular equations). If it was just GREATER to with no equal, then it would actually be a dotted line.

2) You have to shade a certain area of the graph. Since the inequality is saying that it wants you to shade all the y's GREATER than the line, then you shade the portion of the graph ABOVE the line. If it was less than, then you would be shading the area below.

 

[shorty21432]

Ok so you have \(\displaystyle -3x + 2y \ge 6\). Just start solving for it like a regular linear equation, but keep in mind if you ever divide/multiply by a negative number, you have to switch the direction of the inequality!!! However for this particular one, you won't have to switch the inequality, so

\(\displaystyle -3x + 2y \ge 6\)
\(\displaystyle 2y \ge 6 +3x\)
\(\displaystyle y \ge 3 +\frac{3}{2}x\)

You find the x and y intercepts like you normally would (just pretend it's an equal sign for this part). So, obviously the y intercept is 3 (plug in x=0), and I'll let you find out the x intercept (plug in y = 0).

Now when you actually graph it, notice that we have a \(\displaystyle \ge\) sign.

There are two implications:

1) Since it's greater than EQUAL to, then the line you draw will be a SOLID line (just like it is with regular equations). If it was just GREATER to with no equal, then it would actually be a dotted line.

2) You have to shade a certain area of the graph. Since the inequality is saying that it wants you to shade all the y's GREATER than the line, then you shade the portion of the graph ABOVE the line. If it was less than, then you would be shading the area below.

This may be a stupid question but what would the ordered pair for it be? :| Thank you once again

 

[thedarjeeling]

Ordered pair for what?

The y intercept is obviously 3, so the ordered pair is (0,3) for the y intercept. Remember if it's a y intercept, that means that x has to be 0, and the y number is where it hits the y axis.

I'll have to let you figure out the x intercept, just solve the equation \(\displaystyle 0 = 3 + \frac{3}{2}x\)

 

[shorty21432]

Ordered pair for what?

The y intercept is obviously 3, so the ordered pair is (0,3) for the y intercept. Remember if it's a y intercept, that means that x has to be 0, and the y number is where it hits the y axis.

I'll have to let you figure out the x intercept, just solve the equation \(\displaystyle 0 = 3 + \frac{3}{2}x\)

Is it x<or=to2/3-2 so does that make x=-2?? so it would be a point on (-2,0)??

 

[thedarjeeling]

Yes ^_^

Remember when you're doing the graphing, you connect the x and y intercepts in this case with a solid line because you have greater than EQUAL to.

You then need to shade the graph ABOVE the line because it's the set of y coordinates greater than that line.